Couple grade 5 fine thread bolts, a way to ensure they're welded at the right angle, relative to both the steering arm and camber (if your kart has any camber, that is). That's about it. Weld, then let it air cool. Do not quench till it's below 500°.
I say grade 5 because the higher alloy of grade 8 is more prone to cracking at the weld if not done properly.
Here’s a few pictures. Clearly the rim is too long for the spindle. I noticed bmi has a spindle kit with a 6” bolt. I guess something like that would work for the front but what options are there for the dead axle in the back?